Finite Group Databasebeta

← #7711770

Subgroups — #7711770

Order 512.

4356 conjugacy classes of subgroups.

The subgroup lattice has 1118 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60039C214yesmaximal, complemented
2#59619C214yesmaximal, complemented
3#46245C212yesmaximal, complemented
4#46243C211yesmaximal, characteristic, complemented
5#46238C211yesmaximal, characteristic, complemented
6#46230C212yesmaximal, complemented
7#46229C211yesmaximal, characteristic, complemented
8#46226C211yesmaximal, characteristic
9#40407C214yesmaximal, complemented
10#40373C214yesmaximal, complemented
11#38899C214yesmaximal, complemented
12#38898C214yesmaximal, complemented
13#38742C214yesmaximal, complemented
14#38709C214yesmaximal, complemented
15#37612C212yesmaximal, complemented
16#37243C214yesmaximal, complemented
17#36638C212yesmaximal, complemented
18#36589C214yesmaximal, complemented
19#36568C214yesmaximal, complemented
20#35147C214yesmaximal, complemented
21#34526C211yesmaximal, characteristic, complemented
22#34522C211yesmaximal, characteristic, complemented
23C4×#533C211yesmaximal, characteristic, complemented
24C2×#564C2211yescharacteristic
25C2×#562C2211yescharacteristic
26C2×#533C2211yescharacteristic
27#2866C2214yes—
28#2865C2214yes—
29#2864C2212yes—
30#2863C2212yes—
31#2863C2214yes—
32#2861C2212yes—
33#2860C2212yes—
34#2860C2214yes—
35#2855C2212yes—
36#2854C2212yes—
37#2853C2214yes—
38#2852C2214yes—
39#2851C2212yes—
40#2850C2212yes—
41#2844C2212yes—
42#2822C2212yes—
43#2820C2212yes—
44#2820C2212yes—
45#2805C2214yes—
46#2802C2214yes—
47#2798C2214yes—
48#2793C2214yes—
49#2786C2214yes—
50#2777C2214yes—
51#2777C2214yes—
52#2774C2214yes—
53#2772C2214yes—
54#2771C2214yes—
55#2758C2214yes—
56#2758C2214yes—
57#2757C2214yes—
58#2755C2214yes—
59#2742C2214yes—
60#2741C2214yes—
61#2739C2214yes—
62#2720C2214yes—
63#2717C2214yes—
64#2713C2214yes—
65#2711C2214yes—
66#2707C2214yes—
67#2704C2214yes—
68#2700C2214yes—
69#2690C2214yes—
70#2690C2214yes—
71#2690C2214yes—
72#2690C2214yes—
73#2683C2214yes—
74#2676C2214yes—
75#2674C2214yes—
76#2672C2214yes—
77#2654C2214yes—
78#2654C2214yes—
79#2652C2214yes—
80#2650C2214yes—
81#2650C2214yes—
82#2648C2214yes—
83#2638C2214yes—
84#2634C2214yes—
85#2611C2214yes—
86#2605C2214yes—
87#2597C2214yes—
88#2597C2214yes—
89#2597C2214yes—
90#2596C2214yes—
91#2596C2214yes—
92#2596C2214yes—
93#2593C2214yes—
94#2593C2214yes—
95#2588C2214yes—
96#2588C2214yes—
97#2588C2214yes—
98#2588C2214yes—
99#2587C2214yes—
100#2587C2214yes—
101#2587C2214yes—
102#2587C2214yes—
103#2586C2214yes—
104#2586C2214yes—
105#2586C2214yes—
106#2578C2214yes—
107#2577C2214yes—
108#2573C2214yes—
109#2573C2214yes—
110#2573C2214yes—
111#2573C2214yes—
112#2558C2214yes—
113#2558C2214yes—
114#2557C2214yes—
115#2556C2214yes—
116#2556C2214yes—
117#2556C2214yes—
118#2556C2214yes—
119#2533C2214yes—
120#2533C2214yes—
121#2532C2214yes—
122#2532C2214yes—
123#2531C2214yes—
124#2530C2214yes—
125#2525C2214yes—
126#2525C2214yes—
127#2516C2214yes—
128#2516C2214yes—
129#2515C2214yes—
130#2509C2214yes—
131#2490C2214yes—
132#2475C2214yes—
133#2475C2214yes—
134#2474C2214yes—
135#2474C2214yes—
136#2471C2214yes—
137#2470C2214yes—
138#2470C2214yes—
139#2465C2214yes—
140#2465C2214yes—
141#2465C2214yes—
142#2462C2214yes—
143#2462C2214yes—
144#2462C2214yes—
145#2461C2214yes—
146#2455C2214yes—
147#2453C2214yes—
148#2448C2214yes—
149#2447C2214yes—
150#2438C2214yes—
151#2426C2214yes—
152#2421C2214yes—
153#2419C2214yes—
154#2415C2214yes—
155#2382C2211yescharacteristic
156#2382C2211yescharacteristic
157#2382C2212yes—
158#2379C2212yes—
159#2370C2214yes—
160#2370C2214yes—
161#2370C2214yes—
162#2370C2214yes—
163#2370C2214yes—
164#2368C2214yes—
165#2368C2214yes—
166#2368C2214yes—
167#2367C2214yes—
168#2363C2214yes—
169#2362C2214yes—
170#2359C2214yes—
171#2357C2214yes—
172#2347C2214yes—
173#2337C2214yes—
174#2336C2214yes—
175#2336C2214yes—
176#2336C2214yes—
177#2335C2214yes—
178#2335C2214yes—
179#2325C2214yes—
180#2323C2214yes—
181C4×C4⋊Q8C2212yes—
182C4×C4⋊Q8C2212yes—
183C4×#125C2212yes—
184C4×#125C2211yescharacteristic
185C4×#125C2211yescharacteristic
186C4×#125C2211yescharacteristic
187C4×#125C2211yescharacteristic
188C4×#126C2214yes—
189C4×#126C2214yes—
190C4×#126C2214yes—
191C4×#124C2212yes—
192C4×C22⋊Q8C2212yes—
193C4×C22⋊Q8C2214yes—
194C4×C22⋊Q8C2214yes—
195C4×#123C2214yes—
196C4×#121C2212yes—
197#2298C2214yes—
198#2296C2212yes—
199#2295C2212yes—
200#2295C2214yes—
201#2293C2212yes—
202#2290C2214yes—
203#2285C2211yescharacteristic
204C42×Q8C2214yes—
205C4×#117C2212yes—
206C2×C43C2211yescharacteristic
207#564—28no—
208#562—28no—
209#533—28no—
210C2×C4⋊Q8C2312yes—
211C2×#126C2314yes—
212C2×#125C2311yescharacteristic
213C2×#125C2312yes—
214C2×#125C2314yes—
215C2×#125C2314yes—
216C2×#125C2314yes—
217C2×#125C2314yes—
218C2×#125C2314yes—
219C2×#125C2311yescharacteristic
220C2×#124C2312yes—
221C2×#124C2314yes—
222C2×#124C2314yes—
223C2×#123C2314yes—
224C2×#123C2314yes—
225C2×#123C2314yes—
226C2×C22⋊Q8C2314yes—
227C2×C22⋊Q8C2314yes—
228C2×C22⋊Q8C2312yes—
229C2×C22⋊Q8C2314yes—
230C2×C22⋊Q8C2314yes—
231C2×C22⋊Q8C2314yes—
232C2×#121C2314yes—
233C2×#121C2312yes—
234C2×C4×Q8C2314yes—
235C2×C4×Q8C2314yes—
236C2×C4×Q8C2314yes—
237C2×C4×Q8C2312yes—
238C2×C4×D4C2312yes—
239C2×C4×D4C2314yes—
240C2×C4×D4C2314yes—
241C2×#117C2312yes—
242C2×#117C2314yes—
243C2×#117C2314yes—
244C2×#117C2312yes—
245C22×C42C2311yescharacteristic
246C22×C42C2311yescharacteristic
247C22×C42C2312yes—
248C22×C42C2312yes—
249C22×C42C2311yescharacteristic
250#400C2314yes—
251#400C2314yes—
252#400C2314yes—
253#400C2314yes—
254#400C2314yes—
255#400C2314yes—
256#400C2314yes—
257#400C2314yes—
258#400C2314yes—
259#400C2314yes—
260#400C2314yes—
261#400C2314yes—
262#400C2314yes—
263#400C2314yes—
264#400C2314yes—
265#400C2314yes—
266#400C2314yes—
267#400C2314yes—
268#400C2314yes—
269#400C2314yes—
270#399C2314yes—
271#399C2314yes—
272#399C2314yes—
273#399C2314yes—
274#398C2314yes—
275#398C2314yes—
276#398C2314yes—
277#398C2314yes—
278#398C2314yes—
279#398C2314yes—
280#398C2314yes—
281#398C2314yes—
282#398C2314yes—
283#398C2314yes—
284#398C2314yes—
285#397C2314yes—
286#397C2314yes—
287#397C2314yes—
288#397C2314yes—
289#397C2314yes—
290#397C2314yes—
291#397C2314yes—
292#397C2314yes—
293#397C2314yes—
294#397C2314yes—
295#397C2314yes—
296#397C2314yes—
297#397C2314yes—
298#397C2314yes—
299#397C2314yes—
300#396C2314yes—
301#396C2314yes—
302#396C2314yes—
303#396C2314yes—
304#396C2314yes—
305#396C2314yes—
306#396C2314yes—
307#396C2314yes—
308#396C2314yes—
309#396C2314yes—
310#395C2314yes—
311#395C2314yes—
312#395C2314yes—
313#395C2314yes—
314#395C2314yes—
315#395C2314yes—
316#395C2314yes—
317#395C2314yes—
318#395C2314yes—
319#395C2314yes—
320#394C2314yes—
321#394C2314yes—
322#394C2314yes—
323#394C2314yes—
324#394C2314yes—
325#394C2314yes—
326#394C2314yes—
327#393C2314yes—
328#393C2314yes—
329#392C2314yes—
330#391C2314yes—
331#391C2314yes—
332#391C2314yes—
333#391C2314yes—
334#391C2312yes—
335#391C2312yes—
336#391C2314yes—
337#391C2314yes—
338#391C2314yes—
339#391C2314yes—
340#391C2312yes—
341#391C2314yes—
342#391C2312yes—
343#391C2314yes—
344#391C2314yes—
345#390C2314yes—
346#390C2314yes—
347#390C2312yes—
348#390C2312yes—
349#390C2314yes—
350#390C2312yes—
351#390C2312yes—
352#390C2314yes—
353#390C2314yes—
354#389C2312yes—
355#389C2312yes—
356#389C2312yes—
357#389C2312yes—
358#389C2312yes—
359#389C2312yes—
360#389C2314yes—
361#389C2314yes—
362#389C2314yes—
363#389C2314yes—
364#389C2314yes—
365#389C2314yes—
366#389C2312yes—
367#389C2314yes—
368#389C2314yes—
369#389C2314yes—
370#389C2314yes—
371#389C2314yes—
372#389C2314yes—
373#389C2314yes—
374#389C2314yes—
375#389C2314yes—
376#389C2314yes—
377#389C2314yes—
378#389C2314yes—
379#389C2314yes—
380#389C2314yes—
381#389C2312yes—
382#389C2312yes—
383#389C2314yes—
384#389C2312yes—
385#389C2312yes—
386#389C2314yes—
387#389C2312yes—
388#388C2314yes—
389#388C2314yes—
390#388C2314yes—
391#388C2314yes—
392#388C2314yes—
393#388C2314yes—
394#388C2314yes—
395#388C2314yes—
396#388C2314yes—
397#388C2314yes—
398#388C2314yes—
399#388C2314yes—
400#388C2314yes—
401#388C2314yes—
402#388C2314yes—
403#388C2314yes—
404#388C2314yes—
405#388C2314yes—
406#388C2314yes—
407#388C2314yes—
408#388C2314yes—
409#388C2314yes—
410#388C2314yes—
411#388C2314yes—
412#388C2314yes—
413#388C2314yes—
414#388C2314yes—
415#388C2314yes—
416#388C2314yes—
417#388C2314yes—
418#388C2314yes—
419#388C2314yes—
420#388C2314yes—
421#388C2314yes—
422#388C2314yes—
423#388C2314yes—
424#388C2314yes—
425#388C2314yes—
426#388C2314yes—
427#388C2314yes—
428#388C2314yes—
429#388C2314yes—
430#388C2314yes—
431#388C2314yes—
432#388C2314yes—
433#388C2314yes—
434#387C2314yes—
435#387C2314yes—
436#387C2314yes—
437#387C2314yes—
438#387C2314yes—
439#387C2314yes—
440#387C2314yes—
441#387C2314yes—
442#387C2314yes—
443#387C2314yes—
444#387C2314yes—
445#387C2314yes—
446#387C2314yes—
447#387C2314yes—
448#387C2314yes—
449#387C2314yes—
450#387C2314yes—
451#387C2314yes—
452#387C2314yes—
453#387C2314yes—
454#387C2314yes—
455#387C2314yes—
456#387C2314yes—
457#387C2314yes—
458#387C2314yes—
459#387C2314yes—
460#387C2314yes—
461#387C2314yes—
462#387C2314yes—
463#387C2314yes—
464#387C2314yes—
465#387C2314yes—
466#387C2314yes—
467#387C2314yes—
468#387C2314yes—
469#387C2314yes—
470#387C2314yes—
471#387C2314yes—
472#387C2314yes—
473#387C2314yes—
474#387C2314yes—
475#387C2314yes—
476#387C2314yes—
477#387C2314yes—
478#387C2314yes—
479#387C2314yes—
480#387C2314yes—
481#387C2314yes—
482#387C2314yes—
483#387C2314yes—
484#387C2314yes—
485#387C2314yes—
486#387C2314yes—
487#387C2314yes—
488#387C2314yes—
489#387C2314yes—
490#387C2314yes—
491#387C2314yes—
492#386C2314yes—
493#386C2314yes—
494#386C2314yes—
495#386C2314yes—
496#386C2314yes—
497#386C2314yes—
498#386C2314yes—
499#386C2314yes—
500#385C2314yes—
501#385C2314yes—
502#385C2314yes—
503#385C2314yes—
504#385C2314yes—
505#385C2314yes—
506#385C2314yes—
507#385C2314yes—
508#385C2314yes—
509#385C2314yes—
510#385C2314yes—
511#385C2314yes—
512#385C2314yes—
513#385C2314yes—
514#385C2314yes—
515#385C2314yes—
516#384C2312yes—
517#383C2314yes—
518#383C2314yes—
519#383C2314yes—
520#383C2314yes—
521#383C2314yes—
522#382C2311yescharacteristic
523#382C2311yescharacteristic
524#382C2312yes—
525#382C2312yes—
526#382C2314yes—
527#381C2314yes—
528#381C2314yes—
529#381C2314yes—
530#380C2314yes—
531#380C2314yes—
532#380C2312yes—
533#380C2312yes—
534#380C2314yes—
535#380C2314yes—
536C4×C4⋊C4C2314yes—
537C4×C4⋊C4C2314yes—
538C4×C4⋊C4C2314yes—
539C4×C4⋊C4C2314yes—
540C4×C4⋊C4C2314yes—
541C4×C4⋊C4C2314yes—
542C4×C4⋊C4C2314yes—
543C4×C4⋊C4C2314yes—
544C4×C4⋊C4C2314yes—
545C4×C4⋊C4C2312yes—
546C4×C4⋊C4C2312yes—
547C4×C4⋊C4C2312yes—
548C4×C4⋊C4C2312yes—
549C4×C4⋊C4C2314yes—
550C4×C4⋊C4C2314yes—
551C4×C4⋊C4C2314yes—
552C4×C4⋊C4C2314yes—
553C4×C4⋊C4C2312yes—
554C4×C4⋊C4C2312yes—
555C4×C4⋊C4C2314yes—
556C4×C4⋊C4C2314yes—
557C4×C4⋊C4C2314yes—
558C4×C4⋊C4C2314yes—
559C4×C4⋊C4C2314yes—
560C4×C4⋊C4C2314yes—
561C4×C4⋊C4C2314yes—
562C4×C4⋊C4C2314yes—
563C4×C4⋊C4C2314yes—
564C4×C4⋊C4C2314yes—
565C4×C4⋊C4C2314yes—
566C4×C22⋊C4C2314yes—
567C4×C22⋊C4C2314yes—
568C4×C22⋊C4C2314yes—
569C4×C22⋊C4C2314yes—
570C4×C22⋊C4C2314yes—
571C4×C22⋊C4C2314yes—
572C4×C22⋊C4C2314yes—
573C4×C22⋊C4C2314yes—
574C4×C22⋊C4C2314yes—
575C4×C22⋊C4C2314yes—
576C4×C22⋊C4C2314yes—
577C4×C22⋊C4C2314yes—
578C4×C22⋊C4C2314yes—
579#376C2314yes—
580#376C2314yes—
581C2×#95C2314yes—
582C43C2312yes—
583C43C2314yes—
584C43C2311yescharacteristic
585C43C2311yescharacteristic
586C43C2311yescharacteristic
587C43C2311yescharacteristic
588C43C2312yes—
589C22×Q8C2414yes—
590C22×Q8C2412yes—
591C22×Q8C2414yes—
592C22×D4C2412yes—
593C22×D4C2414yes—
594C22×D4C2414yes—
595C23×C4C2411yescharacteristic
596C23×C4C2412yes—
597C23×C4C2412yes—
598C23×C4C2414yes—
599C23×C4C2414yes—
600C23×C4C2411yescharacteristic
601C23×C4C2411yescharacteristic
602C23×C4C2414yes—
603C4⋊Q8—28no—
604#126—216no—
605#125—216no—
606#125—216no—
607#125—216no—
608#125—24no—
609#125—28no—
610#125—48no—
611#125—48no—
612#125#4118yes—
613#124—28no—
614#124—48no—
615#124—48no—
616#123—216no—
617#123—48no—
618#123—48no—
619C22⋊Q8—216no—
620C22⋊Q8—216no—
621C22⋊Q8—48no—
622C22⋊Q8—48no—
623C22⋊Q8—48no—
624C22⋊Q8—44no—
625#121—216no—
626#121—44no—
627C4×Q8—216no—
628C4×Q8—44no—
629C4×Q8—48no—
630C4×Q8—48no—
631C4×D4—44no—
632C4×D4—48no—
633C4×D4—48no—
634#117—28no—
635#117—48no—
636#117—48no—
637#117—44no—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2412yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2412yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2412yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2412yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2412yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2414yes—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2414yes—
684C2×C4⋊C4C2414yes—
685C2×C4⋊C4C2412yes—
686C2×C4⋊C4C2414yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2414yes—
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2414yes—
707C2×C22⋊C4C2414yes—
708C2×C22⋊C4C2414yes—
709C2×C22⋊C4C2414yes—
710C2×C22⋊C4C2414yes—
711C2×C22⋊C4C2414yes—
712C2×C22⋊C4C2414yes—
713C2×C22⋊C4C2414yes—
714C2×C22⋊C4C2414yes—
715C2×C22⋊C4C2414yes—
716C2×C42—24no—
717C2×C42—24no—
718C2×C42—44no—
719C2×C42—44no—
720C2×C42—42no—
721C2×C42C2412yes—
722C2×C42C2414yes—
723C2×C42C2414yes—
724C2×C42C2412yes—
725C2×C42C2412yes—
726C2×C42C2412yes—
727C2×C42C2412yes—
728C2×C42C2414yes—
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731C2×C42C2411yescharacteristic
732C2×C42C2411yescharacteristic
733C2×C42C2414yes—
734C2×C42C2414yes—
735C2×C42C2414yes—
736C2×C42C2414yes—
737C2×C42C2414yes—
738C2×C42C2414yes—
739C2×C42C2414yes—
740C2×C42C2414yes—
741C2×C42C2414yes—
742C2×C42C2414yes—
743C2×C42C2414yes—
744C2×C42C2414yes—
745C2×C42C2411yescharacteristic
746C2×C42C2412yes—
747C2×C42C2412yes—
748C2×C42C2412yes—
749C2×C42C2412yes—
750C2×C42C2411yescharacteristic
751C2×C42C2412yes—
752C2×C42C2411yescharacteristic
753C2×C42C2411yescharacteristic
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2414yes—
763#95C2414yes—
764#95C2414yes—
765#95C2414yes—
766#95C2414yes—
767#95C2414yes—
768#95C2414yes—
769#95C2414yes—
770#95C2414yes—
771#95C2414yes—
772#95C2414yes—
773#95C2414yes—
774#95C2414yes—
775#95C2414yes—
776#95C2414yes—
777#95C2414yes—
778#95C2414yes—
779#95C2414yes—
780#95C2414yes—
781#95C2414yes—
782#95C2414yes—
783#95C2414yes—
784#95C2414yes—
785#95C2414yes—
786#95C2414yes—
787#95C2414yes—
788#95C2414yes—
789#95C2414yes—
790#95C2414yes—
791#95C2414yes—
792#95C2414yes—
793#95C2414yes—
794#95C2414yes—
795#95C2414yes—
796#95C2414yes—
797#95C2414yes—
798#95C2414yes—
799#95C2414yes—
800#95C2414yes—
801#95C2414yes—
802#95C2414yes—
803#95C2414yes—
804#95C2414yes—
805#95C2414yes—
806#95C2414yes—
807#95C2414yes—
808#95C2414yes—
809#95C2414yes—
810#95C2414yes—
811#95C2414yes—
812C24C2514yes—
813C24C2511yescharacteristic
814C2×Q8—28no—
815C2×Q8—24no—
816C2×Q8—28no—
817C2×Q8—44no—
818C2×Q8—42no—
819C2×Q8—42no—
820C2×Q8—44no—
821C2×Q8—44no—
822C2×Q8—44no—
823C2×D4—28no—
824C2×D4—28no—
825C2×D4—24no—
826C2×D4—42no—
827C2×D4—44no—
828C2×D4—42no—
829C2×D4—44no—
830C2×D4—44no—
831C2×D4—44no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—24no—
836C22×C4—24no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—24no—
840C22×C4—24no—
841C22×C4—28no—
842C22×C4—28no—
843C22×C4—42no—
844C22×C4—42no—
845C22×C4—42no—
846C22×C4—42no—
847C22×C4—44no—
848C22×C4—44no—
849C22×C4—44no—
850C22×C4—44no—
851C22×C4—44no—
852C22×C4—44no—
853C22×C4—44no—
854C22×C4C2511yescharacteristic
855C22×C4C2511yescharacteristic
856C22×C4C2514yes—
857C22×C4C2514yes—
858C22×C4C2514yes—
859C22×C4C2514yes—
860C22×C4C2514yes—
861C22×C4C2514yes—
862C22×C4C2512yes—
863C22×C4C2514yes—
864C22×C4C2514yes—
865C22×C4C2514yes—
866C22×C4C2514yes—
867C22×C4C2511yescharacteristic
868C22×C4C2512yes—
869C22×C4C2514yes—
870C22×C4C2511yescharacteristic
871C22×C4C2511yescharacteristic
872C22×C4C2511yescharacteristic
873C22×C4C2512yes—
874C22×C4C2512yes—
875C4⋊C4—24no—
876C4⋊C4—28no—
877C4⋊C4—28no—
878C4⋊C4—28no—
879C4⋊C4—28no—
880C4⋊C4—28no—
881C4⋊C4—28no—
882C4⋊C4—28no—
883C4⋊C4—24no—
884C4⋊C4—24no—
885C4⋊C4—28no—
886C4⋊C4—28no—
887C4⋊C4—28no—
888C4⋊C4—28no—
889C4⋊C4—28no—
890C4⋊C4—28no—
891C4⋊C4—28no—
892C4⋊C4—28no—
893C4⋊C4—28no—
894C4⋊C4—28no—
895C4⋊C4—44no—
896C4⋊C4—42no—
897C4⋊C4—42no—
898C4⋊C4—44no—
899C4⋊C4—42no—
900C4⋊C4—44no—
901C4⋊C4—42no—
902C4⋊C4—44no—
903C4⋊C4—44no—
904C4⋊C4—44no—
905C4⋊C4—44no—
906C4⋊C4—42no—
907C4⋊C4—42no—
908C4⋊C4—44no—
909C4⋊C4—44no—
910C4⋊C4—44no—
911C4⋊C4—44no—
912C4⋊C4—44no—
913C4⋊C4—44no—
914C4⋊C4—44no—
915C4⋊C4—44no—
916C4⋊C4—44no—
917C4⋊C4—44no—
918C4⋊C4—44no—
919C4⋊C4—44no—
920C4⋊C4—44no—
921C4⋊C4—44no—
922C4⋊C4C2×#4118yes—
923C4⋊C4C2×#41116yes—
924C22⋊C4—28no—
925C22⋊C4—28no—
926C22⋊C4—28no—
927C22⋊C4—28no—
928C22⋊C4—28no—
929C22⋊C4—28no—
930C22⋊C4—28no—
931C22⋊C4—28no—
932C22⋊C4—28no—
933C22⋊C4—28no—
934C22⋊C4—28no—
935C22⋊C4—28no—
936C22⋊C4—44no—
937C22⋊C4—44no—
938C22⋊C4—44no—
939C22⋊C4—44no—
940C22⋊C4—44no—
941C22⋊C4—44no—
942C22⋊C4—44no—
943C22⋊C4—44no—
944C22⋊C4—44no—
945C22⋊C4—44no—
946C22⋊C4—44no—
947C22⋊C4—44no—
948C22⋊C4—44no—
949C22⋊C4—44no—
950C22⋊C4—44no—
951C22⋊C4—44no—
952C22⋊C4—44no—
953C42—24no—
954C42—22no—
955C42—28no—
956C42—28no—
957C42—22no—
958C42—22no—
959C42—22no—
960C42—24no—
961C42—24no—
962C42—24no—
963C42—24no—
964C42—28no—
965C42—42no—
966C42—42no—
967C42—42no—
968C42—42no—
969C42—41no—
970C42—41no—
971C42—42no—
972C42—44no—
973C42—44no—
974C42—44no—
975C42—44no—
976C42—44no—
977C42—44no—
978C42—44no—
979C42—44no—
980C42—44no—
981C42—44no—
982C42—44no—
983C42—44no—
984C42C2×#4114yes—
985C422−1+414yes—
986C23—21no—
987C23—21no—
988C23—22no—
989C23—22no—
990C23—24no—
991C23—24no—
992C23—24no—
993C23—24no—
994C23—24no—
995C23—24no—
996C23—24no—
997C23#58512yes—
998C23C2611yescharacteristic
999Q8—416no—
1000Q8—84no—
1001Q8—164no—
1002D4—84no—
1003D4—88no—
1004D4—88no—
1005C2×C4—28no—
1006C2×C4—21no—
1007C2×C4—22no—
1008C2×C4—21no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—21no—
1015C2×C4—22no—
1016C2×C4—24no—
1017C2×C4—21no—
1018C2×C4—22no—
1019C2×C4—24no—
1020C2×C4—24no—
1021C2×C4—24no—
1022C2×C4—24no—
1023C2×C4—24no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—24no—
1027C2×C4—24no—
1028C2×C4—24no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—24no—
1033C2×C4—24no—
1034C2×C4—24no—
1035C2×C4—24no—
1036C2×C4—24no—
1037C2×C4—24no—
1038C2×C4—24no—
1039C2×C4—24no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—24no—
1043C2×C4—24no—
1044C2×C4—24no—
1045C2×C4—24no—
1046C2×C4—24no—
1047C2×C4—24no—
1048C2×C4—24no—
1049C2×C4—24no—
1050C2×C4—24no—
1051C2×C4—24no—
1052C2×C4—24no—
1053C2×C4—24no—
1054C2×C4—24no—
1055C2×C4—24no—
1056C2×C4—24no—
1057C2×C4—48no—
1058C2×C4—48no—
1059C2×C4—44no—
1060C2×C4—44no—
1061C2×C4—88no—
1062C2×C4—88no—
1063C2×C4—164no—
1064C2×C4C22×#4118yes—
1065C2×C4C22×#4112yes—
1066C2×C4C22×#4114yes—
1067C2×C4C2×2−1+412yes—
1068C2×C4C2×2−1+412yes—
1069C2×C4C2×2−1+412yes—
1070C2×C4#58514yes—
1071C2×C4#58514yes—
1072C22—22no—
1073C22—24no—
1074C22—41no—
1075C22—41no—
1076C22—42no—
1077C22—44no—
1078C22—44no—
1079C22—44no—
1080C22—44no—
1081C22—44no—
1082C22—44no—
1083C22—44no—
1084C22C23×#4111yescharacteristic
1085C22C22×2−1+411yescharacteristic
1086C22C2×#58512yes—
1087C22C2×#58512yes—
1088C22C2×#58511yescharacteristic
1089C4—22no—
1090C4—22no—
1091C4—22no—
1092C4—22no—
1093C4—24no—
1094C4—24no—
1095C4—28no—
1096C4—24no—
1097C4—44no—
1098C4—44no—
1099C4—41no—
1100C4—41no—
1101C4—44no—
1102C4—44no—
1103C4—44no—
1104C4—44no—
1105C4—42no—
1106C4—44no—
1107C4—44no—
1108C4—44no—
1109C4—44no—
1110C2—42no—
1111C2—84no—
1112C2#6276111yescharacteristic
1113C2#6276111yescharacteristic
1114C2#6278811yescharacteristic
1115C2#6281012yes—
1116C2#6282812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#46226C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #60039C2semidirect
2. #59619C2semidirect
3. #46245C2semidirect
4. #46243C2semidirect
5. #46238C2semidirect
6. #46230C2semidirect
7. #46229C2semidirect
9. #40407C2semidirect
10. #40373C2semidirect
11. #38899C2semidirect
12. #38898C2semidirect
13. #38742C2semidirect
14. #38709C2semidirect
15. #37612C2semidirect
16. #37243C2semidirect
17. #36638C2semidirect
18. #36589C2semidirect
19. #36568C2semidirect
20. #35147C2semidirect
21. #34526C2semidirect
22. #34522C2semidirect
23. C4×#533C2semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#600392
#596192
#462452
#462432
#462382
#462302
#462292
#462262
#404072
#403732
#388992
#388982
#387422
#387092
#376122
#372432
#366382
#365892
#365682
#351472
#345262
#345222
C4×#5332